Normally, multi-directional and multi-axial bone anchor systems include an outwardly flared opening at the base of a coupling or yoke member through which an anchor member extends. For instance, in U.S. Pat. No. 7,141,051, a spherical or semi-spherical head at one end of the anchor member is trapped within the yoke housing, and a threaded shank portion of the anchor extends out from the bottom of the yoke housing through an outwardly flared opening. The angle of the outwardly directed flare of the opening in the yoke housing is normally configured to allow the screw shank to pivot to a desired angle in any direction around the axis of the yoke. When the patient's anatomy requires the anchor to be fixed at wider angles, the outwardly directed flare of the opening in the yoke housing is designed to be large enough to accommodate the wider angle without the edge of the opening interfering with the positioning of the screw shank or other anchor member. However, an increase in the angle and/or size of the opening in a yoke housing reduces the holding strength of the yoke, since increasing the size of the opening requires removal of material from the housing that would otherwise surround the head portion of the anchor member. Thus, accidental separation of the yoke and anchor member is more likely, increasing the potential for failure of the yoke in securely holding the anchor member therein.